All-solid-state capacitor

ABSTRACT

An all-solid-state capacitor includes an inorganic solid electrolyte; and a pair of current collectors disposed so as to hold it in between. The inorganic solid electrolyte has a polycrystalline structure, and the all-solid-state capacitor satisfies a relationship given as: R 1 &lt;R 2 &lt;R 3 , a relationship given as: C 1 &lt;C 3 , and a relationship given as: C 1 &lt;C 2  in which, R 1 , R 2  and R 3  are resistance components, and R 1  denotes an intragrain resistance of the inorganic solid electrolyte, R 2  denotes a grain-boundary resistance of the inorganic solid electrolyte and R 3  denotes an interfacial resistance between the inorganic solid electrolyte and the current collector, and, C 1 , C 2  and C 3  are capacitance components, and C 1  denotes an intragrain capacity of the inorganic solid electrolyte, C 2  denotes a grain-boundary capacity of the inorganic solid electrolyte and C 3  denotes an interfacial capacity between the inorganic solid electrolyte and the current collector.

TECHNICAL FIELD

The present invention relates to an all-solid-state capacitor thatutilizes an inorganic solid electrolyte having a polycrystallinestructure as an electrolyte.

BACKGROUND ART

Higher level of sophistication and downsizing are demanded in variouselectronic equipment, including information equipment, communicationsequipment, and household electrical appliances, and this trend hascreated a need for each electronic component mounted in electronicequipment to be adapted for the sophistication and downsizing. One ofelectronic components that are mounted in electronic equipment is acapacitor. A capacitance is a performance characteristic demanded in acapacitor, and thus both a high capacitance and reduction in generalsize need to be achieved in a capacitor.

Multilayer ceramic capacitors described in Patent Literatures 1 and 2utilize barium titanate as a dielectric to attain a high relativepermittivity of a dielectric for an increase in capacitance.

In Patent Literature 3, there is described an all-solid-state electricdouble-layer capacitor. An electric double-layer capacitor is intendedto attain a high capacitance by utilizing an electric double layerformed at the interface between an electrolyte and a current collector.Moreover, an all-solid-state capacitor does not use a liquid as anelectrolyte, and is thus free from liquid leakage which may occur in analuminum electrolytic capacitor and an electric double-layer capacitorusing activated carbon.

CITATION LIST Patent Literature

Patent Literature 1: Japanese Examined Patent Publication JP-B2 5046700

Patent Literature 2: Japanese Unexamined Patent Publication JP-A2012-138502

Patent Literature 3: Japanese Unexamined Patent Publication JP-A2008-130844

SUMMARY OF INVENTION Technical Problem

Barium titanate has a relative permittivity in the order of about a fewthousand to ten thousand. Thus, the multilayer ceramic capacitorsdescribed in Patent Literatures 1 and 2 are not capable of achievingboth attainment of a high capacitance and downsizing. Furthermore, inthe electric double-layer capacitor described in Patent Literature 3, acapacitance varies greatly according to the frequency of a voltage to beapplied. Especially in a range of frequencies as low as a few kHz, acapacitance drops sharply as the frequency increases, thus causingdifficulty in attaining stable characteristics.

An object of the invention is to provide an all-solid-state capacitorhaving high capacitance characteristics and low frequency dependence ofcapacitance in a low-frequency range.

Solution to Problem

The invention provides an all-solid-state capacitor including:

an inorganic solid electrolyte; and

a pair of current collectors disposed so as to hold the inorganic solidelectrolyte in between,

the inorganic solid electrolyte having a polycrystalline structure,

the all-solid-state capacitor satisfying a relationship given as:R1<R2<R3, a relationship given as: C1<C3, and a relationship given as:C1<C2,

in which, R1, R2 and R3 are resistance components, and R1 denotes anintragrain resistance of the inorganic solid electrolyte, R2 denotes agrain-boundary resistance of the inorganic solid electrolyte and R3denotes an interfacial resistance between the inorganic solidelectrolyte and the current collector, and,

C1, C2 and C3 are capacitance components, and C1 denotes an intragraincapacity of the inorganic solid electrolyte, C2 denotes a grain-boundarycapacity of the inorganic solid electrolyte and C3 denotes aninterfacial capacity between the inorganic solid electrolyte and thecurrent collector.

Advantageous Effects of Invention

According to the invention, there is provided an all-solid-statecapacitor having high capacitance characteristics and low frequencydependence of capacitance in a low-frequency range.

BRIEF DESCRIPTION OF DRAWINGS

Other and further objects, features, and advantages of the inventionwill be more explicit from the following detailed description taken withreference to the drawings wherein:

FIG. 1 is a sectional view schematically showing the structure of anall-solid-state capacitor 1 in accordance with an embodiment of theinvention;

FIG. 2 is a schematic equivalent circuit diagram used for impedanceanalysis;

FIG. 3 is a graph indicating actual measurement data on LLTO04, LLTO05,and LAGP, and fitting curves obtained by analysis using the equivalentcircuit;

FIG. 4 is a graph indicating the result of actual measurement for thecase of A=428 and B=2959, and the result of the simulation for the caseof A=4 and B=9;

FIG. 5 is a graph indicating the result of actual measurement on LLTO04and the result of the simulation for the case where the grain-boundarycapacity C2 and the interfacial capacity C3 stand at the same value;

FIG. 6 is a graph indicating the result of actual measurement on LLTO04and the result of the simulation for the case where the intragrainresistance R1 takes on a smaller value; and

FIG. 7 is a graph indicating the result of actual measurement on LLTO04and the result of the simulation for the case where the resistancecomponents and the capacity components stand at predeterminedappropriate values.

DESCRIPTION OF EMBODIMENTS

FIG. 1 is a sectional view schematically showing the structure of anall-solid-state capacitor 1 in accordance with an embodiment of theinvention. The all-solid-state capacitor 1 of this embodiment ispreferably given the form of an electric double-layer capacitor whichutilizes an electric double layer, and, the electric double-layercapacitor (hereafter also referred to simply as “capacitor”) 1 comprisesan inorganic solid electrolyte 2 and a pair of current collectors 3A and3B disposed so as to hold the inorganic solid electrolyte 2 in between.The current collectors 3A and 3B are made of a metal material composedpredominantly of at least one of the substances selected from among Au,Ag, and Cu, for example.

The inorganic solid electrolyte 2 has a polycrystalline structure inwhich alkali-metal ions such as Li ions move within crystal grains. Themovement of the alkali-metal ions allows formation of an electric doublelayer at the interface between the current collector 3A, 3B and theinorganic solid electrolyte 2, as well as at crystal grain boundaries,and also allows superposition of dielectric's capacitance under ionicpolarization, interfacial polarization, or orientational polarization incrystal grains or at crystal grain boundaries, thus affording a highcapacitance.

In the electric double-layer capacitor 1, given that, R1, R2 and R3 areelectrical resistance components, and R1 denotes a resistance withincrystal grains of the inorganic solid electrolyte 2, R2 denotes aresistance at crystal grain boundaries of the inorganic solidelectrolyte 2 and R3 denotes a resistance at the interface between theinorganic solid electrolyte 2 and the current collector 3A, 3B, and, C1,C2 and C3 are capacitance components, are C1 denotes a capacity withincrystal grains of the inorganic solid electrolyte 2, C2 denotes acapacity at crystal grain boundaries of the inorganic solid electrolyte2 and C3 denotes a capacity at the interface between the inorganic solidelectrolyte 2 and the current collector 3A, 3B, it is preferable thatR1, R2, R3, C1, C2, and C3 satisfy the following relationships:R1<R2<R3   Formula 1;C1<C3   Formula 2; andC1<C2   Formula 3.

The satisfaction of the Formula 1 makes it possible to define aninterfacial capacity developed in the lowest range of frequencies ofvoltage applied to the electric double-layer capacitor 1 (hereafter alsoreferred to simply as “applied voltage”) as a capacity of the electricdouble-layer capacitor 1, as well as to allow the electric double-layercapacitor 1 to exhibit high insulation performance as a capacitor, andalso exhibit high power storage capability as a power storage device.Moreover, the resistance at crystal grain boundaries (hereafter alsoreferred to simply as “grain-boundary resistance”) is lower than theinterfacial resistance, and the resistance within crystal grains(hereafter also referred to simply as “intragrain resistance”) is lowrelative to the grain-boundary resistance. This brings about the effectof reducing heat generation during the use of the electric double-layercapacitor 1 serving as a capacitor or a power storage device. Theintragrain resistance, in particular, involves heat generation caused byion current within the inorganic solid electrolyte 2, and it is thuspreferable that the intragrain resistance is the lowest among theresistance components.

Moreover, the higher the frequency of applied voltage is, the smallerthe resistance components are, which characterizes an influence exertedupon the capacitance of the electric double-layer capacitor 1. That is,given that the relationship given as: R1<R2<R3 holds, then theinterfacial capacity is dominant in a range of low frequencies ofapplied voltage, but, as the frequency increases, the capacity atcrystal grain boundaries (hereafter also referred to simply as“grain-boundary capacity”) and the capacity within crystal grains(hereafter also referred to simply as “intragrain capacity”)sequentially exert influences in the order named as series capacitanceagainst the interfacial capacity. Thus, a new capacity component whichappears as the frequency of the applied voltage increases is arelatively low capacity, wherefore the capacitance of the electricdouble-layer capacitor 1 drops sharply, signifying frequency dependence.

In this regard, the satisfaction of Formula 3 makes it possible to causethe grain-boundary capacity involving a relatively high capacitance toappear next to the interfacial capacity with increasing frequency, andthereby avoid a sharp decrease in the capacitance in the capacitor.Moreover, the satisfaction of Formulae 2 and 3 makes it possible to keephigh the capacitance of the electric double-layer capacitor 1 based onthe interfacial capacity and the grain-boundary capacity developed in arelatively low frequency range. In addition, by keeping the intragraincapacity which appears at the highest frequency at a minimum, it ispossible to cause frequencies at which the capacitance of the electricdouble-layer capacitor 1 falls to its lowest level to lie in a higherfrequency range.

Examples of the inorganic solid electrolyte 2 that satisfies Formulae 1to 3 include: M1_((2−x)/3) M2_(x)M3O₃ having a perovskite crystalstructure (wherein M1 represents a rare-earth element, M2 represents analkali-metal element, and M3 represents a tetravalent metal element,and, a relationship given as: 0<x≦0.5 is satisfied);Li_(α)Al_(x)Ti_(2−x)(PO₄)_(β) having a NaSICON crystal structure, whichwill hereafter be referred to as “LATP” (wherein relationships given as:0≦x≦0.6; α≧1+x; and 3.0≦β≦3.6 are satisfied);Li_(α(1+x))Al_(x)Ge_(2−x)(PO₄)_(β), which will hereafter be referred toas “LAGP” (wherein relationships given as: 0.4≦x≦0.7; 1.0≦α≦1.2; and3.0≦β≦3.6 are satisfied); Li_(x)A_(y)(B1_(z1)B2_(Z2))O_(t) having agarnet crystal structure (wherein A represents an alkaline-earth metalelement or a rare-earth element, B1 and B2 represent different metalelements that are each one selected from among elements belonging toGroup 3, Group 4, Group 13, and Group 14 in the periodic table, and,relationships given as: 5.5<x<8.0; 2.7<y<3.3; Z1>0; Z2≦0; 1.8<Z1+Z2<2.4;10<t<14 are satisfied); and the aforementioned element containing apredetermined amount of an additive such as a sintering aid.

<Analysis 1>

As exemplary of the inorganic solid electrolyte 2,La_((2-x)/3)Li_(x)TiO₃, which will hereafter be referred to as “LLTO”,in which x=0.50 (hereafter referred to as “LLTO01”), LLTO in whichx=0.42 (hereafter referred to as “LLTO04”), and LLTO05 which is obtainedby adding BaO to LLTO04, and also LAGP (wherein x equals 0.5, α equals1.0, and β equals 3.0) have been subjected to analysis work to check thedependence of a capacitance on the frequency of applied voltage.

Impedance analysis has been conducted by an equivalent circuit on thebasis of the results of impedance measurement on the electricdouble-layer capacitor 1 employing such an inorganic solid electrolyte2. Details of a method for manufacturing the electric double-layercapacitor 1 and a measurement method will be given later on.

FIG. 2 is a schematic equivalent circuit diagram used for impedanceanalysis. As shown in FIG. 2, an equivalent circuit in use is a parallelcircuit including resistance components and capacity components presentwithin crystal grains of the inorganic solid electrolyte 2; at crystalgrain boundaries of the inorganic solid electrolyte 2; and at theinterface between the inorganic solid electrolyte 2 and the currentcollector 3A, 3B. A list of the values of R1, R2, R3, C1, C2, and C3obtained by calculation in impedance analysis is given in Table 1. Inthe invention, resistance is expressed in the unit Ω, and capacity isexpressed in the unit F unless otherwise specified. Although animpedance of each capacity component in an equivalent circuit isgenerally expressed as 1/jωC, in this case, an equivalent circuit modelin which an impedance is expressed as 1/{(j·ω)^(P)·C} was used forimpedance analysis. Also presented in Table 1 are P3, P2, and P1 thatdenote the power of an angular frequency corresponding to theinterfacial capacity, the same corresponding to the grain-boundarycapacity, and the same corresponding to the intragrain capacity,respectively.

TABLE 1 LLTO04 LLTO05 LAGP R1 79 141 335 C1 3.1 × 10⁻¹⁰ 3.6 × 10⁻⁹ 1.7 ×10⁻¹¹ P1  1  0.9  1 R2 2.6 × 10³ 1.5 × 10⁶ 1.7 × 10² C2 2.3 × 10⁻⁷ 7.4 ×10⁻⁸ 2.3 × 10⁻⁹ P2  1  1  1 R3 1.0 × 10²⁰ 2.3 × 10⁶ 1.0 × 10²⁰ C3 7.9 ×10⁻⁶ 2.6 × 10⁻⁵ 2.1 × 10⁻⁵ P3  0.65  0.8  0.80

FIG. 3 is a graph indicating actual measurement data on LLTO04, LLTO05,and LAGP, and fitting curves obtained by analysis using the equivalentcircuit. The abscissa represents angular frequency (rad/s) which equals2π multiplied by normal frequency, and the ordinate representscapacitance equivalent Cp (F). In the graph, actual measurement data onLLTO04, LLTO05, and LAGP and curves fitted for the values of R1, R2, R3,C1, C2, and C3 presented in Table 1 are superimposed. As will beunderstood from the graph, the actual measurement data and the fittingcurves generally conform to each other.

The values of R1, R2, R3, C1, C2, and C3 presented in Table 1, (thesevalues, together with the values of P1, P2, and P3, will hereafter becollectively called “circuitry parameters”) satisfy the relationshipsdefined by Formulae 1, 2, and 3. It will thus be seen that, as thefrequency increases, the interfacial capacity C3, the grain-boundarycapacity C2, and the intragrain capacity C1 are developed as thecapacitance of the electric double-layer capacitor 1.

In the inorganic solid electrolyte 2, it is preferable that a value Awhich is expressed by the following formula (A) falls in the range of0.1 to 100 rad/s:A=1/{R2·(C2·C3)^(1/2)}  (A),

in which R2 denotes the grain-boundary resistance, C2 denotes thegrain-boundary capacity, and C3 denotes the interfacial capacity.

The value A is an approximate measure of a frequency at which thecapacitance of the capacitor drops most rapidly due to the developmentof the grain-boundary resistance R2. In the case where the value A fallsin the range of 0.1 to 100 rad/s, angular frequencies at which thecapacitance drops sharply due to the development of the grain-boundaryresistance R2 can range downwardly from the level of 0.1 to 100 rad/s.In consequence, at angular frequencies of applied voltage rangingupwardly from the level of 0.1 to 100 rad/s, a stable capacitance basedon a composite of the interfacial capacity C3 and the grain-boundarycapacity C2 can be developed as the capacitance of the capacitor, thusreducing the dependence of the capacitance of the electric double-layercapacitor 1 on frequency.

Moreover, it is preferable that a value B which is expressed by thefollowing formula (B) falls in the range of 0.1 to 100 rad/s:B=1/(R2·C2)  (B),

in which R2 denotes the grain-boundary resistance and C2 denotes thegrain-boundary capacity.

The value B is an approximate measure of a frequency at which thereoccurs a transition from a state where the capacitance of the capacitordecreases due to the development of the grain-boundary resistance R2 toa state where a stable capacitance based on a composite of theinterfacial capacity C3 and the grain-boundary capacity C2 can bedeveloped. In the case where the value B falls in the range of 0.1 to100 rad/s, angular frequencies, at which a sharp decrease of thecapacitance that is caused by the development of the grain-boundaryresistance R2 can be reduced by the development of a stable capacitancebased on a composite of the interfacial capacity C3 and thegrain-boundary capacity C2, can range downwardly from the level of 0.1to 100 rad/s. In consequence, at angular frequencies of applied voltageranging upwardly from the level of 0.1 to 100 rad/s, a stablecapacitance based on a composite of the interfacial capacity C3 and thegrain-boundary capacity C2 can be developed as the capacitance of thecapacitor 1, thus reducing the dependence of the capacitance of theelectric double-layer capacitor 1 on frequency.

<Analysis 2>

when in LLTO01, the value A and the value B are calculated on the basisof the circuitry parameters in the manufactured electric double-layercapacitor 1, the value A is 428 rad/s, and the value B is 2959 rad/s. Inrunning a simulation, the grain-boundary capacity C2 and thegrain-boundary resistance R2 were changed to set the value A and thevalue B at 4 rad/s and 9 rad/s, respectively.

FIG. 4 is a graph indicating the result of actual measurement for thecase of A=428 rad/s and B=2959 rad/s, and the result of the simulationfor the case of A=4 rad/s and B=9 rad/s. The indications of the abscissaand the ordinate of FIG. 4 are identical with those shown in FIG. 3.Moreover, circuitry parameters adopted in Analysis 2 are presented inTable 2.

TABLE 2 LLTO01 Simulation R1 82 82 C1 2.6 × 10⁻¹⁰ 2.6 × 10⁻¹⁰ P1  1  1R2 2.6 × 10³ 8.6 × 10⁴ C2 1.3 × 10⁻⁷ 1.3 × 10⁻⁶ P2  1  1 R3 2.2 × 10¹⁹2.2 × 10¹⁹ C3 6.2 × 10⁻⁶ 6.2 × 10⁻⁶ P3  0.63  0.63

The same equivalent circuit as that used in the impedance analysis inAnalysis 1 was used in the simulation. According to the result of thesimulation, in the case of A=4 rad/s and B=9 rad/s, as contrasted toactual measurement data on LLTO01 of A=428 rad/s and B=2959 rad/s, ithas been confirmed that the capacitor can be restrained against anappreciable decrease in capacitance at angular frequencies in the rangeof 1 to 10000 rad/s. Moreover, further reduction of the values A and Bhelps lessen the dependence of the capacitance of the capacitor onfrequency even at angular frequencies ranging downwardly from 1 rad/s.

Such a frequency characteristic can be imparted to the capacitance ofthe capacitor simply by increasing the grain-boundary resistance R2 orthe grain-boundary capacity C2, more specifically, by attaining apolycrystalline structure that is obtained by, for example, reducingamorphous components at the grain boundary phase of LLTO to increasecrystallinity for enhancement in insulation at grain boundaries, orreducing the thickness of an insulating grain-boundary layer to increasethe capacity at grain boundaries.

For example, such a grain boundary phase can be attained by using anexisting technique of designing a sintering aid and a trace additive inconformity with a principal crystalline phase to increase crystallinityof a grain boundary phase of crystallized glass ceramics, or make thegrain boundary phase very thin by using a dielectric material, apiezoelectric material, or the like.

Moreover, in the inorganic solid electrolyte 2, the ratio C2/C3 of thegrain-boundary capacity C2 to the interfacial capacity C3 is preferablygreater than or equal to 0.8. By approximating the value of thegrain-boundary capacity C2 to the value of the interfacial capacity C3,or adjusting the value of the grain-boundary capacity C2 to be greaterthan or equal to the value of the interfacial capacity C3, it ispossible to reduce the dependence of the capacitance of the capacitor 1on frequency. For example, in LLTO04 under Analysis 1, angularfrequencies ranging downwardly from 10 rad/s correspond to a capacitancedefined solely by the interfacial capacity C3; angular frequencies inthe range of 10 to 10000 rad/s correspond to a capacitance in which theinterfacial capacity C3 and the grain-boundary capacity C2 areseries-combined; and angular frequencies ranging upwardly from 10000rad/s correspond to a capacitance in which the interfacial capacity C3,the grain-boundary capacity C2, and the intragrain capacity C1 areseries-combined. By approximating the value of the grain-boundarycapacity C2 to the value of the interfacial capacity C3 to reduce thedifference between the interfacial capacity C3 and the grain-boundarycapacity C2, it is possible to approximate the capacitance of thecapacitor 1 to the interfacial capacity C3 in the range of 10 to 10000rad/s in which the interfacial capacity C3 and the grain-boundarycapacity C2 are dominant, and thereby greatly reduce the dependence ofthe capacitance of the electric double-layer capacitor 1 on frequency atangular frequencies ranging downwardly from 10000 rad/s.

<Analysis 3>

In running a simulation with LLTO04, the grain-boundary capacity C2 andthe interfacial capacity C3 were set at the same value, and, comparisonwas made between the result of the simulation and actual measurementdata. The same equivalent circuit as that used in the impedance analysisin Analysis 1 was used in the simulation.

FIG. 5 is a graph indicating the result of actual measurement on LLTO04and the result of the simulation for the case where the grain-boundarycapacity C2 and the interfacial capacity C3 stand at the same value. Theindications of the abscissa and the ordinate of FIG. 5 are identicalwith those shown in FIG. 3. Moreover, circuitry parameters adopted inAnalysis 3 are presented in Table 3.

TABLE 3 LLTO04 Simulation R1 79 79 C1 3.1 × 10⁻¹⁰ 3.1 × 10⁻¹⁰ P1  1  1R2 2.6 × 10³ 2.6 × 10³ C2 2.3 × 10⁻⁷ 7.9 × 10⁻⁶ P2  1  1 R3 1.0 × 10²⁰1.0 × 10²⁰ C3 7.9 × 10⁻⁶ 7.9 × 10⁻⁶ P3  0.65  0.65

As will be understood from the graph, the dependence of the capacitanceof the capacitor 1 on frequency is analogous to the dependence of thecapacitance of the interfacial capacity C3 on frequency at angularfrequencies ranging up to 10000 rad/s, and it is thus possible to reducea sharp decrease of the capacitance of the capacitor 1 in the range of10 to 100 rad/s with the development of the grain-boundary capacity C2.

The grain-boundary capacity C2 can be increased by raising the capacityof an electric double layer produced at grain boundaries. This isachieved by, for example, attaining a fine structure with thinner grainboundary layers. For example, selection of a material composition ismade in accordance with an existing technique of designing a sinteringaid and a trace additive in conformity with a principal crystallinephase, which is used with a dielectric material or a piezoelectricmaterial having very thin grain boundary layers.

Moreover, it is particularly desirable that the intragrain resistance R1and the grain-boundary capacity C2 satisfy the following formula (C):1/(R1·C2)≧10000 rad/s  (C).

In this case, an angular frequency at which the effect of the intragraincapacity C1 becomes prominent can be set to be greater than or equal to10000 rad/s, wherefore the capacitance of the electric double-layercapacitor 1 at angular frequencies ranging downwardly from 10000 rad/scan be laid to the grain-boundary capacity C2 and thus become lessdependent on frequency.

<Analysis 4>

In running a simulation with LLTO04, the value of the intragrainresistance R1 was reduced, and, comparison was made between the resultof the simulation and actual measurement data.

FIG. 6 is a graph indicating the result of actual measurement on LLTO04and the result of the simulation for the case where the intragrainresistance R1 takes on a smaller value. The indications of the abscissaand the ordinate of FIG. 6 are identical with those shown in FIG. 3.Moreover, circuitry parameters adopted in Analysis 4 are presented inTable 4.

TABLE 4 LLTO04 Simulation R1 79 50 C1 3.12 × 10⁻¹⁰ 3.12 × 10⁻¹⁰ P1  1  1R2 2.57 × 10³ 2.57 × 10³ C2 2.31 × 10⁻⁷ 2.31 × 10⁻⁷ P2  1  1 R3 1.00 ×10²⁰ 1.00 × 10²⁰ C3 7.90 × 10⁻⁶ 7.90 × 10⁻⁶ P3  0.65  0.65

As will be understood from the graph, in LLTO04, a slight reduction inthe value of the intragrain resistance R1 allows frequencies at whichthe effect of the intragrain capacity C1 occurs to lie in a higherfrequency range.

<Analysis 5>

Moreover, it is preferable that the intragrain resistance R1, thegrain-boundary resistance R2, and the grain-boundary capacity C2 satisfythe following formula (D):1/{(C2·(R1·R2)^(1/2)}≧10000 rad/s  (D).

In this case, in addition to the value of the intragrain resistance R1as found in the formula (C), the value of the grain-boundary resistanceR2 is also reduced. This makes it possible to allow frequencies at whichthe effect of the intragrain capacity C1 occurs to lie in an even higherfrequency range, and thereby achieve further reduction of the dependenceof the capacitance on frequency at angular frequencies rangingdownwardly from 10000 rad/s.

In running a simulation with LLTO04, the value of the intragrainresistance R1 was reduced, and, in addition to that, the grain-boundarycapacity C2 and the interfacial capacity C3 were set at the same value,and also the value of the grain-boundary resistance R2 was reduced.Then, comparison was made between the result of the simulation andactual measurement data. FIG. 7 is a graph indicating the result ofactual measurement on LLTO04 and the result of the simulation for thecase where the resistance components and the capacity components standat predetermined appropriate values. The indications of the abscissa andthe ordinate of FIG. 7 are identical with those shown in FIG. 3.Moreover, circuitry parameters adopted in Analysis 5 are presented inTable 5 .

TABLE 5 LLTO04 Simulation R1 79 10 C1 3.1 × 10⁻¹⁰ 3.1 × 10⁻¹⁰ P1  1  1R2 2.6 × 10³ 1.5 × 10¹ C2 2.3 × 10⁻⁷ 7.9 × 10⁻⁶ P2  1  1 R3 1.0 × 10²⁰1.0 × 10²⁰ C3 7.9 × 10⁻⁶ 7.9 × 10⁻⁶ P3  0.65  0.65

As will be understood from the graph, in a case where the value of theintragrain resistance R1 is reduced, and the value of the grain-boundarycapacity C2 is equal to or greater than the value of the interfacialcapacity C3, a reduction in the value of the grain-boundary resistanceR2 allows frequencies at which the effect of the intragrain capacity C1is brought to the fore to lie in an even higher frequency range.

The intragrain resistance R1 results from, for example, scattering ofion current caused by an incommensurate crystal structure such asdislocation in crystal grains, and is augmented with an increase indiscommensuration. As a general rule, by optimizing conditions to besatisfied in firing the inorganic solid electrolyte 2 having apolycrystalline structure, the density of discommensuration such asdislocation in crystal grains of the principal crystalline phase can belowered, thus increasing the crystallinity with consequent attainment ofnearly single-crystal properties. In this way, reduction of theintragrain resistance R1 can be achieved.

Moreover, in the electric double-layer capacitor 1 pursuant to theinvention, the volume resistivity of the inorganic solid electrolyte 2is preferably greater than or equal to 1×10⁵ Ω·cm.

By setting the range of the volume resistivity of the inorganic solidelectrolyte 2 in that way to attain higher insulation against electronconduction, it is possible to increase the capacity of the capacitor 1operated in a low-frequency range, as well as to maintain high powerstorage capability in the capacitor serving as a power storage device.The volume resistivity of the inorganic solid electrolyte 2 can bedetermined by following a step of measuring leakage current which iscaused upon application of DC voltage of 1 to 4 V between the pair ofcurrent collectors 3A and 3B that hold the inorganic solid electrolyte 2in between, and a step of converting the measured leakage current intovolume resistivity for the inorganic solid electrolyte 2.

In the inorganic solid electrolyte 2 having a polycrystalline structure,electron conduction occurs mainly via the grain boundary phase. Thus, toenhance the insulation properties of the inorganic solid electrolyte 2against electron conduction, for example, the crystallinity of the grainboundary phase is increased to suppress electron conduction at the grainboundary phase, thus imparting higher electronic insulation to the grainboundary phase. Such a grain boundary phase can be attained by using anexisting technique of designing a sintering aid and a trace additive inconformity with a principal crystalline phase to increase crystallinityof a grain boundary phase of crystallized glass ceramics, for example.

The thickness of the inorganic solid electrolyte 2 is determined so thatabout several to ten crystal grains exist between the pair of currentcollectors 3A and 3B. This design enables alkali-metal ions such as Liions to mainly move within the crystal grains.

Although there is no particular limitation, for example, the thicknessof the current collector 3A, 3B falls in the range of 0.5 to 3.0 μm.Moreover, the current collector is made of a material composedpredominantly of any one of Au, Ag, and Cu, for example. The currentcollectors 3A and 3B are formed on opposite principal surfaces,respectively, of the inorganic solid electrolyte 2 by means ofsputtering or otherwise, or alternatively, a plurality of inorganicsolid electrolytes 2 and current collectors 3A and 3B are laminated ontop of one another and fired together into a stacked body.

The value P3 in LLTO04 and LAGP presented in Table 1 is less than 1.Thus, a graph line representing the dependence of the capacitance of thecapacitor on frequency is not flat even in a range of frequencies atwhich the interfacial capacity C3 alone serves, and, the developedfrequency dependence is such that the capacitance is decreased bydecrements corresponding to the power of P3−1. It is desirable toapproximate P3 to 1 to reduce such a frequency dependence. This isachieved by obtaining a match between ion conduction in the inorganicsolid electrolyte 2 and electron conduction in the current collectors 3Aand 3B in the vicinity of interfaces. More specifically, in the materialfor constituting the current collectors 3A and 3B such as Au, Ag, or Cu,another metal material or inorganic material is added for optimizationto allow the electron conductivity of the current collectors 3A and 3Bin the vicinity of interfaces to match ion conduction in the inorganicsolid electrolyte 2.

Hereinafter, an example of a method for manufacturing the electricdouble-layer capacitor 1 pursuant to the invention will be described.

In manufacturing the electric double-layer capacitor 1, first, theinorganic solid electrolyte 2 such for example as LLTO is fired, andsubsequently the current collectors 3A and 3B made of a metal materialsuch as Au, Ag, or Cu are formed on the surfaces of the fired inorganicsolid electrolyte 2 with use of an ion sputtering apparatus or the like.For example, the inorganic solid electrolyte 2 can be produced byperforming a step of mixing raw materials, a primary crushing step, acalcining step, a secondary crushing step (the calcining step and thecrushing steps may be repeated several times on an as needed basis), ashaping step, and a firing step in the order named. Conditions to besatisfied in the production, including the calcining temperature, thenumber of calcining steps, and the firing temperature, are determinedproperly in accordance with the material used for the inorganic solidelectrolyte 2. For example, in the case of LLTO, the primary calciningstep is performed under conditions where calcining temperature is 800°C. and retention time is 4 hours; the secondary calcining step isperformed under conditions where calcining temperature is 1150° C. andretention time is 12 hours; and the firing step is performed underconditions where firing temperature is 1250° C. and retention time is 6hours. In this way, the inorganic solid electrolyte 2 is produced.

The following describes the production of samples for actual measurementin each analysis as above described. With use of a polycrystallinesubstance of LLTO having a perovskite crystal structure(La_((2−x)/3)Li_(X)TiO₃) and a polycrystalline substance of LAGP havinga NaSICON crystal structure (Li_(α(1+x))Al_(x)Ge_(2−x)(PO₄)_(β), samplesof the inorganic solid electrolyte 2 were produced.

La₂O powder, Li₂CO₃ powder, TiO₂ powder (rutile type), Al₂O₃ powder,GeO₂ powder, and (NH₄)₂HPO₄ powder that are not less than 99% pure havebeen mixed for preparation so as to attain the composition ratio(element ratio) presented in Table 6 for the case with LLTO, as well asto cause the following relationships to be obtained: x=0.5; α=1.0; andβ=3.0 for the case with LAGP. Then, the mixtures were subjected tocrushing and mixing process (primary crushing step).

After that, the thereby obtained slurry was dried by a rotary evaporatorand then calcined at 800° C. (primary calcining step), as well as at1050° C. (secondary calcining step) for the case with LLTO, or calcinedat 750° C. for the case with LAGP, in the atmosphere. The calcinedpowder has been pulverized (secondary crushing step) so as to have amean particle size of 0.5 to 1.2 μm. In the case of LLTO05, BaCO₃ in anamount of 5% by mass (in oxide (BaO) equivalent) was added to 100% bymass of LLTO04 powder that had undergone the secondary calcining step,and subsequently the powder mixture was subjected to the secondarycrushing step.

A paraffin wax in an amount of 5% by mass was admixed in the powderobtained by the secondary crushing step, and the admixture waspress-molded under a pressure of 1 ton/cm² by a mold press to produce apress-molded body which is 15 mm in diameter and 1.5 mm in thickness.

The press-molded body was fired in the atmosphere under conditions wherethe rate of temperature rise is 400° C./hour; firing temperature is1250° C. (for LLTO) or 850° C. (for LAGP); retention time is 2 to 6hours; and the rate of temperature decrease is 400° C./hour, thusproducing a sintered body in the form of a circular plate which is 13 mmin diameter and 1.3 mm in thickness (inorganic solid electrolyte 2).Conditions to be satisfied in the production of samples of LLTO sinteredbody are presented in Table 6 .

TABLE 6 Firing conditions Rate of Composition ratio Firing Retentiontemperature for preparation temperature time decrease La Li Ti [° C.][hour] [° C./min] LLTO01 0.500 0.500 1 1250 6 400 LLTO04 0.527 0.420 11250 6 400 LLTO05

(Impedance Measurement)

The front and back side of each sample has been polished to amirror-smooth state by #500 to #3000 sandpaper and a #6000 diamondpaste, so that the sample has a thickness of 800 μm. After that, a Auelectrode (current collector) which is 1 cm in diameter was formed oneach of the front and back side by an ion sputtering apparatus(JEOL-JFC-1500).

AC voltage of 500 mV in terms of an rms value of voltage (Bias 0V) wasapplied to each sample formed with the Au electrodes to measure a realpart Z′ and an imaginary part Z″ of impedance. At this time, impedancemeasurement equipment manufactured by Solartron was used for frequenciesranging from 0.01 Hz to 10 MHz, and impedance measurement equipmentmanufactured by Agilent (Model 4294A) was used for frequencies rangingfrom 40 Hz to 110 MHz.

Capacitance Cp (F) was calculated on the basis of the measured real partZ′ and imaginary part Z″ of impedance. The capacitance Cp was calculatedby utilizing the following formula: Cp=Z″/(2πf(Z′²+Z″²)) (wherein frepresents frequency).

(Volume Resistivity Measurement)

The volume resistivity of each sample was derived by applying DC voltageto the Au electrodes of each sample in accordance with a four-terminalmethod, and performing conversion calculation on the basis of thedetected leakage current. Each and every sample exhibited a volumeresistivity of greater than or equal to 6×10⁵ Ω·cm at the appliedvoltage of 1 to 4 V.

The invention may be embodied in other specific forms without departingfrom the spirit or essential characteristics thereof. The presentembodiments are therefore to be considered in all respects asillustrative and not restrictive, the scope of the invention beingindicated by the appended claims rather than by the foregoingdescription and all changes which come within the meaning and the rangeof equivalency of the claims are therefore intended to be embracedtherein.

The invention claimed is:
 1. An all-solid-state capacitor, comprising:an inorganic solid electrolyte; and a pair of current collectorsdisposed so as to hold the inorganic solid electrolyte in between, theinorganic solid electrolyte having a polycrystalline structure, theall-solid-state capacitor satisfying a relationship given as: R1<R2<R3,a relationship given as: C1<C3, and a relationship given as: C1<C2, inwhich, R1, R2 and R3 are resistance components, and R1 denotes anintragrain resistance of the inorganic solid electrolyte, R2 denotes agrain-boundary resistance of the inorganic solid electrolyte and R3denotes an interfacial resistance between the inorganic solidelectrolyte and the current collector, and, C1, C2 and C3 arecapacitance components, and C1 denotes an intragrain capacity of theinorganic solid electrolyte, C2 denotes a grain-boundary capacity of theinorganic solid electrolyte and C3 denotes an interfacial capacitybetween the inorganic solid electrolyte and the current collector,wherein a value B which is expressed by the following formula (B) fallsin a range of 0.1 to 100 rad/s:B=1/(R2·C2)  (B), in which R2 denotes the grain-boundary resistance andC2 denotes the grain-boundary capacity.
 2. The all-solid-state capacitoraccording to claim 1, wherein a value A which is expressed by thefollowing formula (A) falls in a range of 0.1 to 100 rad/s:A=1/{R2·(C2·C3)^(1/2)}  (A), in which R2 denotes the grain-boundaryresistance, C2 denotes the grain-boundary capacity, and C3 denotes theinterfacial capacity.
 3. The all-solid-state capacitor according toclaim 1, wherein a volume resistivity of the inorganic solid electrolyteis greater than or equal to 1×10⁵ Ω·cm.
 4. The all-solid-state capacitoraccording to claim 1, wherein the all-solid-state capacitor is anelectric double-layer capacitor.
 5. An all-solid-state capacitor,comprising: an inorganic solid electrolyte; and a pair of currentcollectors disposed so as to hold the inorganic solid electrolyte inbetween, the inorganic solid electrolyte having a polycrystallinestructure, the all-solid-state capacitor satisfying a relationship givenas: R1<R2 <R3, a relationship given as: C1<C3, and a relationship givenas: C1<C2, in which, R1, R2 and R3 are resistance components, and R1denotes an intragrain resistance of the inorganic solid electrolyte, R2denotes a grain-boundary resistance of the inorganic solid electrolyteand R3 denotes an interfacial resistance between the inorganic solidelectrolyte and the current collector, and, C1, C2 and C3 arecapacitance components, and C1 denotes an intragrain capacity of theinorganic solid electrolyte, C2 denotes a grain-boundary capacity of theinorganic solid electrolyte and C3 denotes an interfacial capacitybetween the inorganic solid electrolyte and the current collector,wherein a ratio C2/C3 of the grain-boundary capacity C2 to theinterfacial capacity C3 is greater than or equal to 0.8.
 6. Anall-solid-state capacitor, comprising: an inorganic solid electrolyte;and a pair of current collectors disposed so as to hold the inorganicsolid electrolyte in between, the inorganic solid electrolyte having apolycrystalline structure, the all-solid-state capacitor satisfying arelationship given as: R1<R2<R3, a relationship given as: C1<C3, and arelationship given as: C1<C2, in which, R1, R2 and R3 are resistancecomponents, and R1 denotes an intragrain resistance of the inorganicsolid electrolyte, R2 denotes a grain-boundary resistance of theinorganic solid electrolyte and R3 denotes an interfacial resistancebetween the inorganic solid electrolyte and the current collector, and,C1, C2 and C3 are capacitance components, and C1 denotes an intragraincapacity of the inorganic solid electrolyte, C2 denotes a grain-boundarycapacity of the inorganic solid electrolyte and C3 denotes aninterfacial capacity between the inorganic solid electrolyte and thecurrent collector, wherein the intragrain resistance R1 and thegrain-boundary capacity C2 satisfy the following formula (C):1/(R1·C2)≧10000 rad/s  (C).